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      Exact milestoning

      1 , 1 , 2
      The Journal of Chemical Physics
      AIP Publishing

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          Abstract

          A new theory and an exact computer algorithm for calculating kinetics and thermodynamic properties of a particle system are described. The algorithm avoids trapping in metastable states, which are typical challenges for Molecular Dynamics (MD) simulations on rough energy landscapes. It is based on the division of the full space into Voronoi cells. Prior knowledge or coarse sampling of space points provides the centers of the Voronoi cells. Short time trajectories are computed between the boundaries of the cells that we call milestones and are used to determine fluxes at the milestones. The flux function, an essential component of the new theory, provides a complete description of the statistical mechanics of the system at the resolution of the milestones. We illustrate the accuracy and efficiency of the exact Milestoning approach by comparing numerical results obtained on a model system using exact Milestoning with the results of long trajectories and with a solution of the corresponding Fokker-Planck equation. The theory uses an equation that resembles the approximate Milestoning method that was introduced in 2004 [A. K. Faradjian and R. Elber, J. Chem. Phys. 120(23), 10880-10889 (2004)]. However, the current formulation is exact and is still significantly more efficient than straightforward MD simulations on the system studied.

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          Most cited references37

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          Computing time scales from reaction coordinates by milestoning.

          An algorithm is presented to compute time scales of complex processes following predetermined milestones along a reaction coordinate. A non-Markovian hopping mechanism is assumed and constructed from underlying microscopic dynamics. General analytical analysis, a pedagogical example, and numerical solutions of the non-Markovian model are presented. No assumption is made in the theoretical derivation on the type of microscopic dynamics along the reaction coordinate. However, the detailed calculations are for Brownian dynamics in which the velocities are uncorrelated in time (but spatial memory remains).
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            Anton, a special-purpose machine for molecular dynamics simulation

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              Variational Approach to Molecular Kinetics.

              The eigenvalues and eigenvectors of the molecular dynamics propagator (or transfer operator) contain the essential information about the molecular thermodynamics and kinetics. This includes the stationary distribution, the metastable states, and state-to-state transition rates. Here, we present a variational approach for computing these dominant eigenvalues and eigenvectors. This approach is analogous to the variational approach used for computing stationary states in quantum mechanics. A corresponding method of linear variation is formulated. It is shown that the matrices needed for the linear variation method are correlation matrices that can be estimated from simple MD simulations for a given basis set. The method proposed here is thus to first define a basis set able to capture the relevant conformational transitions, then compute the respective correlation matrices, and then to compute their dominant eigenvalues and eigenvectors, thus obtaining the key ingredients of the slow kinetics.
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                Author and article information

                Journal
                The Journal of Chemical Physics
                The Journal of Chemical Physics
                AIP Publishing
                0021-9606
                1089-7690
                March 07 2015
                March 07 2015
                : 142
                : 9
                : 094102
                Affiliations
                [1 ]Department of Chemistry, Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, USA
                [2 ]Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, USA
                Article
                10.1063/1.4913399
                4352169
                25747056
                998005a1-3525-4e7f-a25a-d4ee20c13af6
                © 2015
                History

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